A disgruntled professor wants to carry out a hypothesis test to decide whether the mean salaries of faculty in private institutions and public institutions are different. The professor wasn't able to be objective, so she forced her hapless graduate student to take independent random samples of 35 faculty members in private institutions and 31 faculty members in public institutions. (Yes, this professor, though disgruntled, was lucky enough to have a TA.) In private institutions, the average salary (in thousands) was $88, with a sample standard deviation of $26 (thousand). For the public institutions, the average salary (in thousands) was $73, with a standard deviation of $24 (thousand). At the 5% significance level, what is the disgruntled professor's conclusion? Do not assume the population variances are equal.